Comparative study of state-of-the-art matrix-product-state methods for lattice models with large local Hilbert spaces without U(1) symmetry

Lattice models consisting of high-dimensional local degrees freedom without global particle-number conservation constitute an important problem class in the field strongly correlated quantum many-body systems. For instance, they are realized electron-phonon models, cavities, atom-molecule resonance or superconductors. In general, these systems elude a complete analytical treatment and need to be studied using numerical methods where matrix-product states (MPSs) provide flexible generic ansatz class. Typically, MPS algorithms scale at least quadratic dimension Hilbert spaces. Hence, tailored methods, which truncate this dimension, required allow for efficient simulations. Here, we describe compare three state-of-the-art each exploits different approach tackle computational complexity. We analyze properties example Holstein model, performing high-precision calculations as well finite-size-scaling analysis relevant ground-state observables. The performed points phase diagram yielding comprehensive picture approaches.